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Math Help - Partial Derivatives

  1. #1
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    Partial Derivatives

    I have a question about this problem.

    If f(x,y,z) = 0 and g(x,y,z) = 0, show that these three fractions are equal:
    \frac{dx}{\frac{\partial(f,g)}{\partia  l(y,z)}}
    \frac{dy}{\frac{\partial(f,g)}{\partial(z,x)}}
    \frac{dz}{\frac{\partial(f,g)}{\partia  l(x,y)}}

    I know dF and dG both equal zero, but setting them both equal to zero and using Jacobians does not get me to the final answer. I don't know what else to try. Any help would be greatly appreciated!

    I do not know how to get rid of those 68.. numbers.. btw
    Last edited by cuteangel; March 12th 2011 at 05:13 AM. Reason: didnt appear properly
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  2. #2
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    I have a question about this problem.

    If f(x,y,z) = 0 and g(x,y,z) = 0, show that these three fractions are equal:
    \frac{dx}{\frac{\partial(f,g)}{\partial(y,z)}}

    \frac{dy}{\frac{\partial(f,g)}{\partial(z,x)}}

    \frac{dz}{\frac{\partial(f,g)}{\partial(x,y)}}

    I know dF and dG both equal zero, but setting them both equal to zero and using Jacobians does not get me to the final answer. I don't know what else to try. Any help would be greatly appreciated!

    Here is a better version!
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  3. #3
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    Quote Originally Posted by cuteangel View Post

    If f(x,y,z) = 0 and g(x,y,z) = 0, show that these three fractions are equal:
    \frac{dx}{\frac{\partial(f,g)}{\partial(y,z)}}

    \frac{dy}{\frac{\partial(f,g)}{\partial(z,x)}}

    \frac{dz}{\frac{\partial(f,g)}{\partial(x,y)}}
    Okay, I took the cross product of the gradient of f and the gradient of g and found the partial derivative jacobians in the denominator. This vector will be parallel to the intersection of the tangent planes if the curve C is given as the intersection of f(x,y,z)=0 and g(x,y,z)=0. However, I suppose to find the equation I am after I need to take the cross product of these partial derivatives with (dx, dy, dz). But I do not know why or how this would apply. Any help would be greatly appreciated!
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